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Homework Help: Help with Eigenvalues problem

  1. Jul 21, 2009 #1
    1. The problem statement, all variables and given/known data


    If Ttheta is a rotation of the Euclidean plane R2 counterclockwise through an angle theta, then T can be represented by an orthogonal matrix P whose eigenvalues are lambda1 = 1 and lambda2 = -1.

    2. Relevant equations

    3. The attempt at a solution

    Just checking to see if my thinking is right. I say false because the representation of T in orthogonal coordinates would require a transformation requiring trigonometric functions. This wouldn't be a linear transformation and therefore cannot be treated as an eigensystem.

    Yes? No?
  2. jcsd
  3. Jul 21, 2009 #2


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    Gold Member

    Re: Eigenvalues

    The answer is false, but I can't figure out what you're trying to say for your reasoning. Rotations are linear functions of the plane, and can be represented my matrices. You can either consider determinants, or try to demonstrate no rotation can do what is proposed to the two eigenvectors
  4. Jul 21, 2009 #3


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    Gold Member

    Re: Eigenvalues

    Using sines and cosines is still a linear transformation.

    Think of it this way, what is the determinant of a matrix such that it's eigenvalues are -1,1?
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